If everyone rode a bicycle, there would be a lot more bicycle deaths. According to table 6 of this study, https://injuryprevention.bmj.com/content/21/1/47, 71.4% of the fatalities involved motor vehicles. If we apply that percentage to todays number of bicyclist deaths (900) in the USA, we get 257 deaths that do not involve motor vehicles.

If we add congestion into the mix since everyone is bicycling, I imagine a higher number of accidents would occur. Right now an estimated 67 million people in the USA ride a bicycle for an estimated 15 billion hours combined per year. 228 million licensed drivers times 290 average hours on the road equals 66 billion hours per year. Let us assume the bicyclists will have to spend three times more travel time due to lower speed of bicycles. That equals roughly 200 billion hours of bicycling per year. 200 billion hours divided by 15 billion equals 13.3. 900 257 deaths per 15 billion hours equals 3,341 deaths per year. The average number of deaths per year from automobile crashes for the last few years is about 36,000.

Even if this is a conservative estimate. I think it is safe to say you are essentially correct.